微结构光纤中的模间干涉及光腔的模式耦合
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摘要
包层微结构调整的灵活性,使得微结构光纤(Microstructure fiber, MF)的光学特性明显的不同于传统光纤。这些不同于传统光纤的显著特征使得微结构光纤成为光学领域的一个研究热点。本论文对微结构光纤的一些特性进行了初步的探讨。
首先,对微结构光纤的研究概况进行了一般的综述。其中包括微结构光纤概念的提出,和传统光纤相比的异同,微结构光纤色散的多样性,微结构光纤中的偏振和双折射,微结构光纤在非线性光学中的应用以及微结构光纤制作材料和制作方法的多样性,微结构光纤中的模间干涉等。
其次,简要介绍了用于研究微结构光纤模式及其模间干涉的几种方法。其中包括:等效折射率方法、局域化函数方法、全矢量平面波展开法、双正交基矢方法、多极化方法、Fourier展开法、有限微分方法和有限元方法等。这些方法各有优点和缺点,根据研究对象和精度的不同,在实际工作中可以灵活选取合适的研究方法。
然后,利用等效折射率方法,对不同结构参数微结构光纤的不同模式的色散特性进行了研究。结果发现,微结构光纤的模式及其色散特性灵敏地依赖于它的结构参数。多模微结构光纤中不同模式的零色散点分布在一个波段上,使得在零色散点附近才能发生的一些非线性现象更加容易显现。例如多模微结构光纤中各种非线性联合效应产生的超连续光谱就是一个典型的例证。
再然后,重点研究了微结构光纤中的模间干涉现象。利用等效折射率方法对仅仅支持两个导模的一种微结构光纤中的模间干涉现象进行了研究,理论计算和文献中报道的实验测量结果符合的比较好。它说明了这种计算方法的可行性,更为重要的是,理论计算还指出了微结构光纤中,频率域的双模干涉中存在精细结构,精细结构的出现是微结构包层灵活调整的结果。这些精细结构使干涉测量的精度提高了一个数量级。接下来解释了我们课题组制作的一种微结构光纤中的奇异现象:将钛蓝宝石飞秒激光脉冲耦合到一种微结构光纤中,在一定的波段产生连续的光谱之后,沿着光纤轴线方向,出现了某些颜色强度极大的一些谱线的准周期分布。在制作微结构光纤的早期阶段,曾经在空气孔无规则分布的多芯微结构光纤中观测到类似的现象,当时解释为光纤无规则空气孔不对称导致的与偏振相关的干涉现象。而这次拉制的光纤尺寸均匀性很好,对其产生的类似现象需要重新给出解释。数值计算表明,这根微结构光纤仅仅支持最低阶的四个导模,而这四个导模之间的模间干涉计算结果能够比较好的说明这种现象。最后把微结构光纤中的多模干涉特征和传统光波导中的多模干涉特征进行了对比,指出了微结构光纤中多模干涉现象的潜在应用领域。
论文的最后一部分,研究了光腔间的模式耦合特性。对入射腔基横模到次级光腔基横模、一阶横模、二阶横模和三阶横模的功率耦合系数进行了研究,给出了这些耦合系数对光腔轴线间的平行移位、光腔轴线间的相对倾斜的依赖关系的解析表达式。最终给出了这些模式耦合系数达到最大值的条件。理论计算对光学腔体的调节有一定的指导作用。
Due to the tailoring flexibility of the cladding microstructure, the optical characteristics of microstructure fiber (hereinafter referred to as MF) are obviously different from those of the traditional fiber. The MF has become a heatedly discussed topic in the optical filed due to these characteristics. The thesis attempts to conduct an elementary research concerning some characteristics of MF.
Firstly, a general review about the research situation on the area of MF has been given. The review includes the introduction of the concept of MF, the similarities and differences between the MF and the traditional fiber, variety of the dispersion characteristics of MF, polarization and birefringence in MF, MF application in nonlinear optics and the multiplicity of the MF fabrication materials and the fabrication methods, intermodal interference in MF, etc.
Then, a number of methods for the study of mode and intermodal interference in MF have been introduced briefly. The methods include: the effective-index method, the localized function method, the full vector plane wave decomposition method, the biorthonormal-basis method, the multi-pole method, the Fourier decomposition method, the finite-difference method, and the finite element method, etc. Each method has its respective advantages and disadvantages. One can choose appropriate method with flexibility depending on the research object and the requirement of calculation accuracy in the actual research work.
Further more, the different mode dispersion characteristics of various structure parameter MF have been studied using the effective-index method. The results indicate that the mode and dispersion characteristics of MF are determined by its structure parameter sensitively. The zero dispersion points of different modes in multi-mode MF distribute on one wavelength region. Some nonlinear effects, which can only take place in the vicinity of the zero dispersion point, take place more easily in the multi-mode MF. The supercontinuum spectrum generated by the combination of various nonlinear effects in the multi-mode MF is a typical example.
Intermodal interference in MF has been studied intensively in the following section. The intermodal interference phenomenon in a MF which only supports two guided modes has been studied firstly by using the effective index method. The theoretic result coincides well with the experimental measurement reported in the reference. This coincidence confirms that the theoretical method chosen is a feasible one for the present research. More importantly, the fine structure in two-mode intermodal interference in frequency domain is predicted by the theoretical calculation. The fine structure is induced by the flexibility tailoring of the cladding microstructure. The fine structure has improved the interference measurement preciseness by one degree. Then, a novel phenomenon in the MF which is made by our group has been explained. A continuum spectral is generated in a certain wavelength region when a femtosecond pulse generated by the Ti:sapphire laser is coupled into a MF. Then, along the direction of the fiber core, a pseudo-periodic distribution of some colors intensively spectral line in some wavelength emerged. A similar phenomenon has been observed in a random distribution air hole multicore MF at the beginning stage of MF fabrication. At that time, the phenomenon was considered as the result of polarization-related interference induced by the asymmetry of the random air holes. But now, the MF is well symmetric, the phenomenon should be explained by other mechanism. Numerical calculation shows that the MF can only support four guided modes. The intermodal interference in the four mode MF can very well explain the phenomenon. Finally, a contrast and comparison of multi-mode intermodal interference between the MF and the traditional waveguide has been conducted. The potential application areas of multi-mode intermodal interference in MF have been shown.
The characteristic of the mode coupling between cavities has been studied in the last section of the doctoral thesis. The fractions of power coupling between the injecting cavity's fundamental mode and the following cavity’s fundamental mode, the first transverse mode, second transverse mode, and third transverse mode have been studied. The dependence of these fractions of power coupling on the relative offset and tilting between the cavity axes are given in an analytical expression. The conditions that must be satisfied for these fractions of power coupling to get the maximum are given finally. This piece of theoretical work may be used as a guideline in the process of optical cavity adjustment.
首先,对微结构光纤的研究概况进行了一般的综述。其中包括微结构光纤概念的提出,和传统光纤相比的异同,微结构光纤色散的多样性,微结构光纤中的偏振和双折射,微结构光纤在非线性光学中的应用以及微结构光纤制作材料和制作方法的多样性,微结构光纤中的模间干涉等。
其次,简要介绍了用于研究微结构光纤模式及其模间干涉的几种方法。其中包括:等效折射率方法、局域化函数方法、全矢量平面波展开法、双正交基矢方法、多极化方法、Fourier展开法、有限微分方法和有限元方法等。这些方法各有优点和缺点,根据研究对象和精度的不同,在实际工作中可以灵活选取合适的研究方法。
然后,利用等效折射率方法,对不同结构参数微结构光纤的不同模式的色散特性进行了研究。结果发现,微结构光纤的模式及其色散特性灵敏地依赖于它的结构参数。多模微结构光纤中不同模式的零色散点分布在一个波段上,使得在零色散点附近才能发生的一些非线性现象更加容易显现。例如多模微结构光纤中各种非线性联合效应产生的超连续光谱就是一个典型的例证。
再然后,重点研究了微结构光纤中的模间干涉现象。利用等效折射率方法对仅仅支持两个导模的一种微结构光纤中的模间干涉现象进行了研究,理论计算和文献中报道的实验测量结果符合的比较好。它说明了这种计算方法的可行性,更为重要的是,理论计算还指出了微结构光纤中,频率域的双模干涉中存在精细结构,精细结构的出现是微结构包层灵活调整的结果。这些精细结构使干涉测量的精度提高了一个数量级。接下来解释了我们课题组制作的一种微结构光纤中的奇异现象:将钛蓝宝石飞秒激光脉冲耦合到一种微结构光纤中,在一定的波段产生连续的光谱之后,沿着光纤轴线方向,出现了某些颜色强度极大的一些谱线的准周期分布。在制作微结构光纤的早期阶段,曾经在空气孔无规则分布的多芯微结构光纤中观测到类似的现象,当时解释为光纤无规则空气孔不对称导致的与偏振相关的干涉现象。而这次拉制的光纤尺寸均匀性很好,对其产生的类似现象需要重新给出解释。数值计算表明,这根微结构光纤仅仅支持最低阶的四个导模,而这四个导模之间的模间干涉计算结果能够比较好的说明这种现象。最后把微结构光纤中的多模干涉特征和传统光波导中的多模干涉特征进行了对比,指出了微结构光纤中多模干涉现象的潜在应用领域。
论文的最后一部分,研究了光腔间的模式耦合特性。对入射腔基横模到次级光腔基横模、一阶横模、二阶横模和三阶横模的功率耦合系数进行了研究,给出了这些耦合系数对光腔轴线间的平行移位、光腔轴线间的相对倾斜的依赖关系的解析表达式。最终给出了这些模式耦合系数达到最大值的条件。理论计算对光学腔体的调节有一定的指导作用。
Due to the tailoring flexibility of the cladding microstructure, the optical characteristics of microstructure fiber (hereinafter referred to as MF) are obviously different from those of the traditional fiber. The MF has become a heatedly discussed topic in the optical filed due to these characteristics. The thesis attempts to conduct an elementary research concerning some characteristics of MF.
Firstly, a general review about the research situation on the area of MF has been given. The review includes the introduction of the concept of MF, the similarities and differences between the MF and the traditional fiber, variety of the dispersion characteristics of MF, polarization and birefringence in MF, MF application in nonlinear optics and the multiplicity of the MF fabrication materials and the fabrication methods, intermodal interference in MF, etc.
Then, a number of methods for the study of mode and intermodal interference in MF have been introduced briefly. The methods include: the effective-index method, the localized function method, the full vector plane wave decomposition method, the biorthonormal-basis method, the multi-pole method, the Fourier decomposition method, the finite-difference method, and the finite element method, etc. Each method has its respective advantages and disadvantages. One can choose appropriate method with flexibility depending on the research object and the requirement of calculation accuracy in the actual research work.
Further more, the different mode dispersion characteristics of various structure parameter MF have been studied using the effective-index method. The results indicate that the mode and dispersion characteristics of MF are determined by its structure parameter sensitively. The zero dispersion points of different modes in multi-mode MF distribute on one wavelength region. Some nonlinear effects, which can only take place in the vicinity of the zero dispersion point, take place more easily in the multi-mode MF. The supercontinuum spectrum generated by the combination of various nonlinear effects in the multi-mode MF is a typical example.
Intermodal interference in MF has been studied intensively in the following section. The intermodal interference phenomenon in a MF which only supports two guided modes has been studied firstly by using the effective index method. The theoretic result coincides well with the experimental measurement reported in the reference. This coincidence confirms that the theoretical method chosen is a feasible one for the present research. More importantly, the fine structure in two-mode intermodal interference in frequency domain is predicted by the theoretical calculation. The fine structure is induced by the flexibility tailoring of the cladding microstructure. The fine structure has improved the interference measurement preciseness by one degree. Then, a novel phenomenon in the MF which is made by our group has been explained. A continuum spectral is generated in a certain wavelength region when a femtosecond pulse generated by the Ti:sapphire laser is coupled into a MF. Then, along the direction of the fiber core, a pseudo-periodic distribution of some colors intensively spectral line in some wavelength emerged. A similar phenomenon has been observed in a random distribution air hole multicore MF at the beginning stage of MF fabrication. At that time, the phenomenon was considered as the result of polarization-related interference induced by the asymmetry of the random air holes. But now, the MF is well symmetric, the phenomenon should be explained by other mechanism. Numerical calculation shows that the MF can only support four guided modes. The intermodal interference in the four mode MF can very well explain the phenomenon. Finally, a contrast and comparison of multi-mode intermodal interference between the MF and the traditional waveguide has been conducted. The potential application areas of multi-mode intermodal interference in MF have been shown.
The characteristic of the mode coupling between cavities has been studied in the last section of the doctoral thesis. The fractions of power coupling between the injecting cavity's fundamental mode and the following cavity’s fundamental mode, the first transverse mode, second transverse mode, and third transverse mode have been studied. The dependence of these fractions of power coupling on the relative offset and tilting between the cavity axes are given in an analytical expression. The conditions that must be satisfied for these fractions of power coupling to get the maximum are given finally. This piece of theoretical work may be used as a guideline in the process of optical cavity adjustment.
引文
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83 S. Hilaire, D. Pagnoux, P. Roy, and S. Février. Numerical Study of Single Mode Er-Doped Microstructured Fibers: Influence of Geometrical Parameters on Amplifier Performances. Opt. Express, 2006, 14(22):10865-10877
84 M. Moenster, P. Glas, G. Steinmeyer, R. Iliew, N. Lebedev, R. Wedell, and M. Bretschneider. Femtosecond Neodymium-Doped Microstructure Fiber Laser. Opt. Express, 2005, 13(21):8671-8677
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87 Y. Logvin, V. P. Kalosha, and H. Anis. Third-Order Dispersion Impact on Mode-Locking Regimes of Yb-Doped Fiber Laser with Photonic Bandgap Fiber for Dispersion Compensation. Opt. Express, 2007, 15(3):985-991
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102 A. Mussot, M. Beaugeois, M. Bouazaoui, and T. Sylvestre. Tailoring CW Supercontinuum Generation in Microstructured Fibers with Two-Zero Dispersion Wavelengths. Opt. Express, 2007, 15(18):11553-11563
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